Treadmill Pace = Outdoor Pace?

Today I decided to use the treadmill for the first time in about six months. It was just way too hot out this morning. I did a hard six miles and for some reason it felt harder than my outdoor runs. This probably has to do with the mental aspect...it was very boring! But, as I was running, I started wondering if the pace I was doing on the treadmill would be the same if I were running outside. I figured it wouldn't be, considering no wind resistance, etc. on the treadmill. So after doing some research, I found a handy pace conversion chart. I was running at 7.5 speed on the treadmill at a 0% incline (an 8 min. mile on the treadmill), so outdoors it would be the equivalent of an 8:20 mile. Check out the site...http://www.hillrunner.com/training/tmillchart.php